Three-dimensional traffic data flexible interpolation method and device

Abstract

The invention discloses a three-dimensional traffic data flexible interpolation method and device, and belongs to the technical field of traffic data processing. The method comprises the following steps: acquiring missing three-dimensional traffic data # imgabs0 # and an index set omega of known data; a three-dimensional tensor nuclear norm. 3DTNN and a three-dimensional total variation. 3DTV are set; a three-dimensional traffic data interpolation model GCLSNL is constructed; an auxiliary variable # imgabs1 # is set, and a three-dimensional traffic data interpolation model GCLSNL is reconstructed; and according to the reconstructed three-dimensional traffic data interpolation model GCLSNL, solving to obtain the three-dimensional traffic data after data completion. According to the method, the global structure, the local features and the non-local textures of the data can be kept at the same time, missing data can be flexibly recovered, and the precision of traffic data interpolation can be effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of traffic data processing, and in particular, relates to a three-dimensional traffic data flexible interpolation method and device. Background Art

[0002] Traffic network data has the characteristics of large data scale, multi-network and multi-source, complex heterogeneity, diverse collection methods, high dimension and complex structure. With the rapid development of Internet of Things technology and information technology, more and more traffic data can be collected and stored. For example, the ring coil vehicle detector installed on the road can obtain data such as traffic flow, occupancy, speed, etc. of the current monitored road surface. These data can be used to build intelligent transportation systems and improve traffic conditions. However, the traffic data collected in the real world is usually incomplete. For example, the detector may fail, the storage device may fail, and the data transmitted from the detector to the storage device may be distorted, which will cause data loss. The loss of data will seriously affect the overall quality of the data and hinder the effective use of data by upper-level applications in the intelligent transportation system. Therefore, it is necessary to interpolate the traffic data.

[0003] Various matrix-based traffic data interpolation techniques have been proposed in the prior art, such as the K-nearest neighbor method, the Kriging method, the principal component analysis and its extension method, the joint method of the Toeplitz matrix and the graph Laplacian matrix, etc. However, the above matrix-based methods ignore the strong daily cycle patterns and similarities in traffic data, which are reflected in the relevant cycle dependencies between working days and non-working days. In order to better consider the high-dimensional characteristics of the data, many tensor-based techniques have emerged in recent years to interpolate missing values. Researchers proposed an interpolation framework based on the matrix nuclear norm and tensor expansion operator (SNN), called HaLRTC. Furthermore, researchers replaced the above matrix nuclear norm with the Schattenp-norm to improve the accuracy of traffic data interpolation. However, the application of the tensor expansion operator destroys the inherent structure in the traffic data, making it difficult for the SNN-based method to better represent the low rank of the tensor. In order to address the above shortcomings, the tensor nuclear norm is introduced using tensor singular value decomposition (T-SVD) for interpolation data. Since this method can well maintain the intrinsic structure of the data, more and more studies use T-SVD for traffic data recovery. However, the T-SVD-based method lacks flexibility in dealing with the correlation between different modes. At the same time, the above methods rely on the global information of traffic data, and the interpolation accuracy cannot meet the analysis requirements in extreme cases. Summary of the invention

[0004] The purpose of the embodiments of the present invention is to provide a flexible interpolation method and device for three-dimensional traffic data, aiming to simultaneously maintain the global structure, local features and non-local texture of the data, flexibly restore missing data, and effectively improve the accuracy of traffic data interpolation.

[0005] In order to solve the above technical problems, the present invention is achieved through the following technical solutions:

[0006] In a first aspect, the present invention provides a flexible interpolation method for three-dimensional traffic data, comprising the following steps:

[0007] S100: Obtaining missing 3D traffic data and the index set Ω of known data;

[0008] S200: Set the three-dimensional tensor nuclear norm ∥·∥ 3DTNN and 3D total variation ∥·∥ 3DTV ;

[0009] S300: constructing a three-dimensional traffic data interpolation model GCLSNL, wherein the mathematical expression of the three-dimensional traffic data interpolation model GCLSNL is:

[0010]

[0011] in, is the minimization operator, For the missing 3D traffic data, is the known data observed, ∥·∥ 3DTNN is the nuclear norm of the three-dimensional tensor, ∥·∥ 3DTV is the three-dimensional total variation, is the non-local regularization term under the plug-and-play framework, ω is the adjustment parameter, st means that the condition is satisfied, is the projection operator, Ω is the index set of known data;

[0012] S400: Setting auxiliary variables The three-dimensional traffic data interpolation model GCLSNL is reconstructed as:

[0013]

[0014] in, It is expressed as:

[0015]

[0016] Step S500: Solving and obtaining the three-dimensional traffic data after data completion according to the reconstructed three-dimensional traffic data interpolation model GCLSNL.

[0017] Furthermore, in step S200, the expression of the three-dimensional tensor nuclear norm is as follows:

[0018]

[0019] in, represents any three-dimensional tensor, represents the sum of k from 1 to 3, μ k is the kth μ, ||·|| TNN,k Represents the tensor nuclear norm of mode-k, which is the tensor of all modes-k The sum of the singular values ​​of .

[0020] Furthermore, in step S200, the expression of the three-dimensional total variation is as follows:

[0021]

[0022] in, represents any three-dimensional tensor, λ 1,2,3 represents the weight parameter, ||·||1 represents the l1-norm of the tensor, Represents the difference operator in three directions, and the expression is as follows:

[0023]

[0024] in, Respectively Forward slice of represents the identity matrix of size n1×n1, represents a zero matrix of size n1×n1, Represents a matrix D of size n1×n1, expressed as follows:

[0025]

[0026] Furthermore, the step S500 specifically includes:

[0027] Step S501: Initialization make and is a zero tensor, and is the Lagrange multiplier, input parameter set μ, θ, λ, β, ω, index set Ω, and maximum number of iterations t max , let t = 0;

[0028] Step S502: Update By minimizing the optimization problem, we get:

[0029]

[0030] The closed-form solution of the above equation can be obtained by the following formula:

[0031]

[0032] Where τ = μ k / θ k is the threshold, and t-SVT(·) is obtained by the following theorem:

[0033]

[0034]

[0035] Step S503: Update

[0036]

[0037] Among them, soft ρ (·) is the soft threshold operator, defined as:

[0038]

[0039] Among them, sign(·) is the sign function;

[0040] Step S504: Update The formula is as follows;

[0041]

[0042] in, BM3D is the BM3D non-local regularization term in the plug-and-play framework;

[0043] Step S505: Update according to Definition, The closed form solution of the subproblem is as follows:

[0044]

[0045] in, It is found by the following formula:

[0046]

[0047] Step S506: Update Lagrange multipliers and The formula is as follows;

[0048]

[0049] Step S507: Determine the convergence condition. If it does not converge, go back to step S502. If it converges, obtain the three-dimensional traffic data after interpolation.

[0050] In a second aspect, the present invention provides a three-dimensional traffic data flexible interpolation device, comprising:

[0051] Acquisition device for acquiring missing three-dimensional traffic data and the index set Ω of known data;

[0052] The first setting module is used to set the three-dimensional tensor nuclear norm ∥·∥ 3DTNN and 3D total variation ∥·∥ 3DTV ;

[0053] The construction module is used to construct a three-dimensional traffic data interpolation model GCLSNL. The mathematical expression of the three-dimensional traffic data interpolation model GCLSNL is:

[0054]

[0055] in, is the minimization operator, For the missing 3D traffic data, is the known data observed, ∥·∥ 3DTNN is the nuclear norm of the three-dimensional tensor, ∥·∥ 3DTV is the three-dimensional total variation, is the non-local regularization term under the plug-and-play framework, ω is the adjustment parameter, st means that the condition is satisfied, is the projection operator, Ω is the index set of known data;

[0056] The second setting module is used to set auxiliary variables The three-dimensional traffic data interpolation model GCLSNL is reconstructed as:

[0057]

[0058] in, It is expressed as:

[0059]

[0060] The solution module is used to solve the three-dimensional traffic data after data completion according to the reconstructed three-dimensional traffic data interpolation model GCLSNL.

[0061] Furthermore, the solution module includes an initialization unit, a first updating unit, a second updating unit, a third updating unit, a fourth updating unit, a fifth updating unit and a determination unit.

[0062] The initialization unit is specifically used to initialize make and is a zero tensor, and is the Lagrange multiplier, input parameter set μ, θ, λ, β, ω, index set Ω, and maximum number of iterations t max , let t = 0;

[0063] The first updating unit is used to update By minimizing the following optimization problem, we get:

[0064]

[0065] The closed-form solution of the above equation can be obtained by the following formula:

[0066]

[0067] Where τ = μ k / θ k is the threshold, and t-SVT(·) is obtained by the following theorem:

[0068]

[0069]

[0070] The second updating unit is used to update

[0071]

[0072] Among them, soft ρ (·) is the soft threshold operator, defined as:

[0073]

[0074] Among them, sign(·) is the sign function;

[0075] The third updating unit is used to update The formula is as follows;

[0076]

[0077] in, BM3D is the BM3D non-local regularization term in the plug-and-play framework;

[0078] The fourth updating unit is used to update according to Definition, The closed form solution of the subproblem is as follows:

[0079]

[0080] in, It is found by the following formula:

[0081]

[0082] The fifth updating unit is used to update the Lagrange multiplier and The formula is as follows;

[0083]

[0084] The determination unit is specifically used to determine the convergence condition. If it does not converge, it returns to execute the first updating unit; if it converges, it obtains the three-dimensional traffic data after interpolation data.

[0085] The beneficial effects of the present invention are:

[0086] The present invention provides a method and device for flexible interpolation of three-dimensional traffic data, firstly obtaining missing three-dimensional traffic data and the index set Ω of the known data, through the three-dimensional tensor nuclear norm ∥·∥ 3DTNN The missing traffic data is restored by low-rank constraints, and the three-dimensional total variation ∥·∥ 3DTV Mining the smoothness characteristics of adjacent data in three directions of traffic data, and exploring the non-local self-similarity characteristics of traffic data through plug-and-play non-local regularization terms; then constructing a three-dimensional traffic data interpolation model GCLSNL; then setting auxiliary variables The three-dimensional traffic data interpolation model GCLSNL is reconstructed. Finally, according to the reconstructed three-dimensional traffic data interpolation model GCLSNL, global low rank, smooth regularization and non-local structure are explored to solve the problems of random and structured traffic data missing. In addition, the proposed three-dimensional traffic data interpolation model GCLSNL is processed by an efficient algorithm based on the alternating direction multiplier method, which can simultaneously maintain the global structure, local features and non-local texture of the data, flexibly restore missing data, and effectively improve the accuracy of traffic data interpolation.

[0087] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0089] Figure 1It is a schematic diagram of the implementation process of a flexible interpolation method for three-dimensional traffic data provided by an embodiment of the present invention;

[0090] Figure 2 The quantitative comparison results of the proposed GCLSNL and the contrasting methods in the GTL dataset are shown;

[0091] Figure 3 The quantitative comparison results of the proposed GCLSNL and the contrasting methods in the PeMS dataset are shown;

[0092] Figure 4 It is a functional block diagram of a three-dimensional traffic data flexible interpolation device provided by an embodiment of the present invention.

[0093] Reference numerals in the figures:

[0094] Acquisition device 100; First setting module 200; Construction module 300;

[0095] A second setting module 400; and a solution module 500. DETAILED DESCRIPTION

[0096] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention.

[0097] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0098] Example 1

[0099] like Figure 1 As shown, a flexible interpolation method for three-dimensional traffic data provided by an embodiment of the present invention may include the following steps:

[0100] Step S100: Obtaining missing 3D traffic data And the index set Ω of known data.

[0101] In this embodiment, the three-dimensional traffic data It mainly includes two datasets: GTL dataset and PeMS dataset. The GTL dataset comes from the Urban Laboratory in Grenoble, France. The dataset comes from 21 road segments, covers 91 days, and the sampling interval is 5 minutes. The PeMS dataset comes from the PeMS database. Traffic sensors are deployed on highways in California. The dataset comes from 108 road segments, covers 36 working days, and each data point is collected at an interval of 5 minutes.

[0102] On the other hand, this embodiment designs three types of data missing scenarios to obtain the three-dimensional traffic data of the missing data. And the index set Ω of known data are:

[0103] Scenario 1 is random missing: given complete traffic data By randomly By replacing the elements in with 0, we can get a new simulated tensor The number of replaced elements is determined by the missing rate (MR). In the simulation, we set MR to 40%, 50%, 60%, 70%, and 80%.

[0104] Scenario 2 is fiber deficiency: By replacing By replacing the elements in the modal-k fiber with 0, we can get the simulated traffic data Among them, select As an example missing case, the missing rate MR is set to be the same as scenario 1.

[0105] Scenario 3: Slice missing: Compared with the first two missing scenarios, slice missing represents a more complex situation. Simulated traffic data is by converting from The elements in the i-th horizontal slice of are replaced by 0, that is, And set the miss rate MR to be the same as scenario 1.

[0106] Step S200: Setting the three-dimensional tensor nuclear norm ∥·∥ 3DTNN and 3D total variation ∥·∥ 3DTV .

[0107] Specifically, the expression of the three-dimensional tensor nuclear norm is as follows:

[0108]

[0109] in, represents any three-dimensional tensor, represents the sum of k from 1 to 3, μ k is the kth μ, ||·|| TNN,k Represents the tensor nuclear norm of mode-k, which is the tensor of all modes-k The sum of the singular values ​​of .

[0110] In this embodiment, the three-dimensional tensor nuclear norm ∥·∥ 3DTNN Perform low-rank constraint restoration on missing traffic data.

[0111] On the other hand, the expression of the three-dimensional total variation is as follows:

[0112]

[0113] in, represents any three-dimensional tensor, λ 1,2,3 represents the weight parameter, ||·||1 represents the l1-norm of the tensor, Represents the difference operator in three directions, and the expression is as follows:

[0114]

[0115] in, Respectively Forward slice of represents the identity matrix of size n1×n1, represents a zero matrix of size n1×n1, Represents a matrix D of size n1×n1, expressed as follows:

[0116]

[0117] In this embodiment, the three-dimensional total variation ∥·∥ 3DTV Mining the smoothness characteristics of adjacent data in three directions of traffic data.

[0118] Step S300: constructing a three-dimensional traffic data interpolation model.

[0119] The three-dimensional traffic data interpolation model is GCLSNL, and its mathematical expression is:

[0120]

[0121] in, is the minimization operator, For the missing 3D traffic data, is the known data observed, ∥·∥ 3DTNN is the nuclear norm of the three-dimensional tensor, ∥·∥ 3DTV is the three-dimensional total variation, is the non-local regularization term under the plug-and-play framework, ω is the adjustment parameter, st means that the condition is satisfied, is the projection operator, and Ω is the index set of known data.

[0122] In this embodiment, the non-local self-similarity characteristics of traffic data are explored through a plug-and-play non-local regularization term.

[0123] Step S400: setting auxiliary variables and reconstructing the three-dimensional traffic data interpolation model.

[0124] Among them, set the auxiliary variables to The three-dimensional traffic data interpolation model GCLSNL is reconstructed as:

[0125]

[0126] in, It is expressed as:

[0127]

[0128] Step S500: solving and obtaining the three-dimensional traffic data after data completion according to the reconstructed three-dimensional traffic data interpolation model.

[0129] Wherein, the step S500 specifically includes:

[0130] Step S501: Initialization make and is a zero tensor, and is the Lagrange multiplier, input parameter set μ, θ, λ, β, ω, index set Ω, and maximum number of iterations t max , let t = 0;

[0131] Step S502: Update By minimizing the following optimization problem, we get:

[0132]

[0133] The closed-form solution of the above equation can be obtained by the following formula:

[0134]

[0135] Where τ = μ k / θ k is the threshold, and t-SVT(·) is obtained by the following theorem:

[0136]

[0137]

[0138] Step S503: Update

[0139]

[0140] Among them, soft ρ (·) is the soft threshold operator, defined as:

[0141]

[0142] Among them, sign(·) is the sign function;

[0143] Step S504: Update The formula is as follows;

[0144]

[0145] in, BM3D is the BM3D non-local regularization term in the plug-and-play framework;

[0146] Step S505: Update according to Definition, The closed form solution of the subproblem is as follows:

[0147]

[0148] in, It is found by the following formula:

[0149]

[0150] Step S506: Update Lagrange multipliers and The formula is as follows;

[0151]

[0152] Step S507: Determine the convergence condition. If it does not converge, go back to step S502. If it converges, obtain the three-dimensional traffic data after interpolation.

[0153] In order to evaluate the performance of GCLSNL proposed in this embodiment, a comparative example is introduced, and the parameters in the comparative example are adjusted as recommended to achieve the best performance. It should be noted that the data models used in the comparative example can be HaLRTC, T-SVD, SpBCD and STH-LRTC. Among them, HaLRTC is a low-rank tensor completion framework that realizes data completion by expanding the operator and minimizing the matrix nuclear norm. T-SVD: This low-rank completion model is based on the concept of low tube rank and realizes convex relaxation of tube rank by minimizing the tensor nuclear norm. SpBCD: This model is based on the tensor Schatten-p norm and minimizes the norm by adopting quadratic penalty and block coordinate descent method. STH-LRTC: This is a tensor completion method based on the spatiotemporal Hankel delay embedding framework.

[0154] The present invention selects the root mean square error (RMSE) and the mean absolute percentage error (MAPE) as the performance indicators for evaluating the proposed method and the comparison method. The expressions of RMSE and MAPE are as follows:

[0155]

[0156] in and They are actual and estimated values, Represents the total number of missing data. Smaller RMSE and MAPE values ​​indicate better results of traffic data completion.

[0157] like Figure 2 and Figure 3 As shown in the figure, the quantitative comparison results of the proposed GCLSNL and the comparative examples under the GTL dataset and the PeMS dataset are shown, and the best results are highlighted in bold. It can be seen that under different missing scenarios, the GCLSNL method proposed in the embodiment of the present invention has lower RMSE and MAPE values ​​compared with other advanced comparison methods. It can be seen that the GCLSNL proposed in the embodiment of the present invention has certain advantages in RMSE and MAPE.

[0158] Specifically, there is a large difference between the recovery results of HaLRTC and T-SVD and the true values. This shows that relying solely on global low rank is not enough to recover data details. In addition, when the missing values ​​present low rank characteristics, HaLRTC and T-SVD will also fail in traffic data interpolation. Overall, our proposed method is also closer to the real data than the baseline model. In contrast, the superiority and reliability of the method proposed in this embodiment can be seen, especially in the case of missing fibers and missing slices. This is because the GCLSNL method captures low rank in three directions, explores local information in three modes, and considers the non-local structure of each slice. In summary, according to the evaluation of RMSE and MAPE and the results of visual comparison, the proposed method performs superiorly.

[0159] Example 2

[0160] like Figure 4 As shown, a three-dimensional traffic data flexible interpolation device provided by an embodiment of the present invention may include an acquisition device 100, a first setting module 200, a construction module 300, a second setting module 400 and a solution module 500.

[0161] The acquisition device 100 is used to acquire missing three-dimensional traffic data. And the index set Ω of known data.

[0162] The first setting module 200 is used to set the three-dimensional tensor nuclear norm ∥·∥ 3DTNN and 3D total variation ∥·∥ 3DTV .

[0163] The construction module 300 is used to construct a three-dimensional traffic data interpolation model GCLSNL. The mathematical expression of the three-dimensional traffic data interpolation model GCLSNL is:

[0164]

[0165] in, is the minimization operator, For the missing 3D traffic data, is the known data observed, ∥·∥ 3DTNN is the nuclear norm of the three-dimensional tensor, ∥·∥ 3DTV is the three-dimensional total variation, is the non-local regularization term under the plug-and-play framework, ω is the adjustment parameter, st means that the condition is satisfied, is the projection operator, and Ω is the index set of known data.

[0166] The second setting module 400 is used to set auxiliary variables The three-dimensional traffic data interpolation model GCLSNL is reconstructed as:

[0167]

[0168] in, It is expressed as:

[0169]

[0170] The solving module 500 is used to solve the three-dimensional traffic data after data completion according to the reconstructed three-dimensional traffic data interpolation model GCLSNL.

[0171] The solution module 500 specifically includes an initialization unit, a first updating unit, a second updating unit, a third updating unit, a fourth updating unit, a fifth updating unit and a determination unit.

[0172] Specifically, the initialization unit is specifically used to initialize make and is a zero tensor, and is the Lagrange multiplier, input parameter set μ, θ, λ, β, ω, index set Ω, and maximum number of iterations t max , let t = 0;

[0173] The first updating unit is used to update By minimizing the following optimization problem, we get:

[0174]

[0175] The closed-form solution of the above equation can be obtained by the following formula:

[0176]

[0177] Where τ = μ k / θ k is the threshold, and t-SVT(·) is obtained by the following theorem:

[0178]

[0179]

[0180] The second updating unit is used to update

[0181]

[0182] Among them, soft ρ (·) is the soft threshold operator, defined as:

[0183]

[0184] Among them, sign(·) is the sign function;

[0185] The third updating unit is used to update The formula is as follows;

[0186]

[0187] in, BM3D is the BM3D non-local regularization term in the plug-and-play framework;

[0188] The fourth updating unit is used to update according to Definition, The closed form solution of the subproblem is as follows:

[0189]

[0190] in, It is found by the following formula:

[0191]

[0192] The fifth updating unit is used to update the Lagrange multiplier and The formula is as follows;

[0193]

[0194] The determination unit is specifically used to determine the convergence condition. If it does not converge, it returns to execute the first updating unit; if it converges, it obtains the three-dimensional traffic data after interpolation data.

[0195] It should be noted that the implementation principle and technical effects of the device provided in the embodiment of the present invention are the same as those of the aforementioned method embodiment. For the sake of brief description, for matters not mentioned in the device embodiment, reference may be made to the corresponding contents in the aforementioned method embodiment.

[0196] In summary, the embodiment of the present invention first obtains the missing three-dimensional traffic data and the index set Ω of the known data, through the three-dimensional tensor nuclear norm ∥·∥ 3DTNN The missing traffic data is restored by low-rank constraints, and the three-dimensional total variation ∥·∥ 3DTV Mining the smoothness characteristics of adjacent data in three directions of traffic data, and exploring the non-local self-similarity characteristics of traffic data through plug-and-play non-local regularization terms; then constructing a three-dimensional traffic data interpolation model GCLSNL; then setting auxiliary variables The three-dimensional traffic data interpolation model GCLSNL is reconstructed. Finally, according to the reconstructed three-dimensional traffic data interpolation model GCLSNL, global low rank, smooth regularization and non-local structure are explored to solve the problems of random and structured traffic data missing. In addition, by processing the proposed three-dimensional traffic data interpolation model GCLSNL with an efficient algorithm based on the alternating direction multiplier method, a lower root mean square error and mean absolute percentage error can be obtained, so that the global structure, local features and non-local texture of the data can be maintained at the same time, the missing data can be flexibly restored, and the accuracy of traffic data interpolation can be effectively improved.

[0197] In the embodiments provided by the present invention, it should be understood that the disclosed devices and methods can also be implemented in other ways. The device embodiments described above are merely schematic. For example, the flowcharts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the devices, methods and computer program products according to multiple embodiments of the present invention. In this regard, each box in the flowchart or block diagram can represent a module, a program segment or a part of a code, and the module, program segment or a part of the code contains one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, and the combination of boxes in the block diagram and / or flowchart can be implemented with a dedicated hardware-based system that performs a specified function or action, or can be implemented with a combination of dedicated hardware and computer instructions.

[0198] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A flexible interpolation method for three-dimensional traffic data, characterized in that: The following steps are involved: S100: Obtaining missing 3D traffic data and the index set Ω of known data; S200: Set the three-dimensional tensor nuclear norm ∥·∥ 3DTNN and 3D total variation ∥·∥ 3DTV ; S300: constructing a three-dimensional traffic data interpolation model GCLSNL, wherein the mathematical expression of the three-dimensional traffic data interpolation model GCLSNL is: in, is the minimization operator, For the missing 3D traffic data, is the known data observed, ∥·∥ 3DTNN is the nuclear norm of the three-dimensional tensor, ∥·∥ 3DTV is the three-dimensional total variation, is the non-local regularization term under the plug-and-play framework, ω is the adjustment parameter, st means that the condition is satisfied, is the projection operator, Ω is the index set of known data; S400: Setting auxiliary variables The three-dimensional traffic data interpolation model GCLSNL is reconstructed as: in, It is expressed as: Step S500: Solving and obtaining the three-dimensional traffic data after data completion according to the reconstructed three-dimensional traffic data interpolation model GCLSNL.

2. The flexible interpolation method for three-dimensional traffic data according to claim 1, characterized in that: In step S200, the expression of the three-dimensional tensor nuclear norm is as follows: in, represents any three-dimensional tensor, represents the sum of k from 1 to 3, μ k is the kth μ, ||·|| TNN,k Represents the tensor nuclear norm of mode-k, which is the tensor of all modes-k The sum of the singular values ​​of .

3. The flexible interpolation method for three-dimensional traffic data according to claim 1, characterized in that: In step S200, the expression of the three-dimensional total variation is as follows: in, represents any three-dimensional tensor, λ 1,2,3 represents the weight parameter, ||·||1 represents the l1-norm of the tensor, Represents the difference operator in three directions, and the expression is as follows: in, Respectively Forward slice of represents the identity matrix of size n1×n1, represents a zero matrix of size n1×n1, Represents a matrix D of size n1×n1, expressed as follows:

4. The flexible interpolation method for three-dimensional traffic data according to claim 1, characterized in that: The step S500 specifically includes: Step S501: Initialization make and is a zero tensor, and is the Lagrange multiplier, input parameter set μ, θ, λ, β, ω, index set Ω, and maximum number of iterations t max , let t = 0; Step S502: Update By minimizing the optimization problem, we get: The closed-form solution of the above equation can be obtained by the following formula: Where τ = μ k / θ k is the threshold, and t-SVT(·) is obtained by the following theorem: Step S503: Update Among them, soft ρ (·) is the soft threshold operator, defined as: Among them, sign(·) is the sign function; Step S504: Update The formula is as follows; in, BM3D is the BM3D non-local regularization term in the plug-and-play framework; Step S505: Update according to Definition, The closed form solution of the subproblem is as follows: in, It is found by the following formula: Step S506: Update Lagrange multipliers and The formula is as follows; Step S507: Determine the convergence condition. If it does not converge, go back to step S502. If it converges, obtain the three-dimensional traffic data after interpolation.

5. A three-dimensional traffic data flexible interpolation device, characterized in that: The device comprises: Acquisition device for acquiring missing three-dimensional traffic data and the index set Ω of known data; The first setting module is used to set the three-dimensional tensor nuclear norm ∥·∥ 3DTNN and 3D total variation ∥·∥ 3DTV ; The construction module is used to construct a three-dimensional traffic data interpolation model GCLSNL. The mathematical expression of the three-dimensional traffic data interpolation model GCLSNL is: in, is the minimization operator, For the missing 3D traffic data, is the known data observed, ∥·∥ 3DTNN is the nuclear norm of the three-dimensional tensor, ∥·∥ 3DTV is the three-dimensional total variation, is the non-local regularization term under the plug-and-play framework, ω is the adjustment parameter, st means that the condition is satisfied, is the projection operator, Ω is the index set of known data; The second setting module is used to set auxiliary variables The three-dimensional traffic data interpolation model GCLSNL is reconstructed as: in, It is expressed as: The solution module is used to solve the three-dimensional traffic data after data completion according to the reconstructed three-dimensional traffic data interpolation model GCLSNL.

6. The three-dimensional traffic data flexible interpolation device according to claim 5, characterized in that: The solution module includes an initialization unit, a first updating unit, a second updating unit, a third updating unit, a fourth updating unit, a fifth updating unit and a determination unit. The initialization unit is specifically used to initialize make and is a zero tensor, and is the Lagrange multiplier, input parameter set μ, θ, λ, β, ω, index set Ω, and maximum number of iterations t max , let t = 0; The first updating unit is used to update , by minimizing the following optimization problem, we get: The closed-form solution of the above equation can be obtained by the following formula: Where τ = μ k / θ k is the threshold, and t-SVT(·) is obtained by the following theorem: The second updating unit is used to update Among them, soft ρ (·) is the soft threshold operator, defined as: Among them, sign(·) is the sign function; The third updating unit is used to update The formula is as follows; in, BM3D is the BM3D non-local regularization term in the plug-and-play framework; The fourth updating unit is used to update according to Definition, The closed form solution of the subproblem is as follows: in, It is found by the following formula: The fifth updating unit is used to update the Lagrange multiplier and The formula is as follows; The determination unit is specifically used to determine the convergence condition. If it does not converge, it returns to execute the first updating unit; if it converges, it obtains the three-dimensional traffic data after interpolation data.

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